Evolution of axions in the presence of primordial magnetic fields

TL;DR

This paper investigates how primordial magnetic fields influence axion evolution from the QCD phase transition, finding that axions can still serve as viable cold dark matter candidates despite weak Primakoff effects.

Contribution

It provides a detailed derivation of the coupled evolution equations for axions and magnetic fields considering universe expansion and magnetic spectra, confirming previous estimates of weak Primakoff effects.

Findings

Axion zero mode amplitude remains sufficient for dark matter candidacy.

Primakoff effect has a weak impact on axion and magnetic field dynamics.

Results align with previous estimates when including Hubble expansion effects.

Abstract

We study the evolution of axions interacting with primordial magnetic fields (PMFs) starting just from the QCD phase transition in the expanding universe. This interaction is owing to the Primakoff effect. Adopting the zero mode approximation for axions, we derive the system of equations for axions and magnetic fields, where the expansion of the universe and the spectra of magnetic fields are accounted for exactly. We find that the contribution of the Primakoff effect to the dynamics of axions and magnetic fields is rather weak. It confirms some previous estimates leading to analogous conclusions, when accounting here for the Hubble expansion both for an uniform axion field and non-uniform PMFs using Fourier spectra for their energy and helicity densities. We solve the corresponding system of the evolution equations and find that the axion zero mode, when evolving during radiation era, has its amplitude at the level sufficient for that axion to be a good candidate for the cold dark matter.